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Adaptive frequency oscillator... The left plot of this figure represents the evolution of ω(t) when the adaptive Hopf oscillator is coupled to the z variable of the Lorenz attractor. The right plot represents the z variable of the Lorenz attractor. We clearly see that the adaptive Hopf oscillators can correctly learn the pseudo-frequency of the Lorenz attractor. See the text for more details. ... Plots of the frequency of the oscillations of the Van der Pol oscillator according to ω. Here α=50. There are two plots, for the dotted line the oscillator is not coupled and for the plain line the oscillator is coupled to F=sin30t. The strength of coupling is ϵ=2. We clearly see basins of phase-locking, the main one for frequency of oscillations 30. The other major basins appear each 30n (dotted horizontal lines). We also notice small entrainment basins for some frequencies of the form 30pq. For a more detailed discussion of these results refer to the text. ... We show the adaptation of the Van der Pol oscillator to the frequencies of various input signals: (a) a simple sinusoidal input (F=sin(40t)), (b) a sinusoidal input with uniformly distributed noise (F=sin(40t)+uniform noise in [−0.5,0.5]), (c) a square input (F=square(40t)) and (d) a sawtooth input (F=sawtooth(40t)). For each experiment, we set ϵ=0.7 and α=100 and we show three plots. The right one shows the evolution of ω(t). The upper left graph is a plot of the oscillations, x, of the system, at the beginning of the learning. The lower graph shows the oscillations at the end of learning. In both graphs, we also plotted the input signal (dashed). In each experiment, ω converges to ω≃49.4, which corresponds to oscillations with a frequency of 40 rad s−1 like the input and thus the oscillator correctly adapts its frequency to the frequency of the input. ... Frequency spectra of the Van der Pol oscillator, both plotted with ω=10. The left figure is an oscillator with α=10 and on the right the nonlinearity is higher, α=50. On the y-axis we plotted the square root of the power intensity, in order to be able to see smaller frequency components. ... This figure shows the convergence of ω for several initial frequencies. The Van der Pol oscillator is perturbed by F=sin(30t), with coupling ϵ=0.7, α=50. We clearly see that the convergence directly depends on the initial conditions and as expected the different kinds of convergence correspond to the several entrainment basins of Fig. 7.
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(a) Spin maser oscillation signal observed in a time span of 24 hours. (b) Transient pattern in the initial spin maser oscillation. (c) Steady state oscillation after the transient settled. The signals shown in the ordinates represent the beat between the spin detection signal and a 36.12 Hz fixed frequency reference signal for a lock-in amplifier. ... (a) Fourier spectrum obtained when the newly introduced current source was used for the oscillator operation. The measurement time was 3×104 seconds. (b) Fourier spectrum obtained when the previous current source was used for the oscillator operation. The measurement time was 1×104 seconds. ... Nuclear spin oscillator... Steady state oscillations observed at three low frequencies: (a) ν0=17.7 Hz, (b) ν0=8.9 Hz, (c) ν0=2.5 Hz. The strength of the static field adopted in the individual operations are indicated in the respective panels. ... Frequency precision... Frequency precision of the spin oscillation. The abscissa represents the standard deviation of the frequency ν determined by fitting a function ϕ(t)=2πνt+ϕ0 to the observed precession phases ϕ from t=0 to t=Tm. Solid, dotted and dashed lines are the presentation of three cases with power laws σν∝Tm−3/2, σν∝Tm−1, and σν∝Tm−1/2 respectively.
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Dominant frequencies of 10mm nozzle. ... Condensation regime map by Cho et al. [1] (C–chugging, TC—transitional region from chugging to CO, CO—condensation oscillation, SC—stable condensation, BCO—bubble condensation oscillation, IOC—interfacial oscillation condensation). ... Condensation oscillation... Frequencies at different test conditions—250kgm−2s−1. ... Frequency... Prediction accuracy of simultaneous equations for oscillation frequency. ... Frequencies at different test conditions—300kgm−2s−1.
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Spatial frequencies distributions... Ragged oscillation death... The phase synchronization domains (areas enclosed by the red lines) and the OD regions (black areas) in the parameter space of ε-δω for a ring of coupled Rossler systems with different frequency distributions: (a) G={1,2,3,4,5,6,7,8}, (b) G={1,4,3,6,2,8,5,7}, and (c) G={1,2,3,6,8,4,7,5}. N=8. The ragged OD sates are clear in (b) and (c) within a certain interval of δω indicated by two vertical dashed lines. In all three insets, the values of ωj are plotted for given ω0=0 and δω=N. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) ... The bifurcation diagram and the largest Lyapunov exponent λ of the coupled Rossler oscillators versus the coupling strength ε with the same spatial arrangement of natural frequencies as in Fig. 1(a)–(c), respectively for δω=0.58. The bifurcation diagram is realized by the soft of XPPAUT [33] where the black dots are fixed points and the red dots are the maximum and minimum values of x1 for the stable periodic solution while the blue dots means the max/min values of x1 for the unstable periodical states. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) ... The critical curves of OD domain from analysis in N coupled Landau–Stuart oscillators for different N’s: (a) N=2, (b) N=3, and (c)–(e) N=4 for G={1,2,3,4},G={1,2,4,3}, and G={1,3,2,4}, respectively. The ragged OD domain is clear in (d). The numerical results with points within the domains perfectly verify the analytical results. ... The OD regions in the parameter space of ε-δω for a ring of coupled Rossler systems with different frequency distributions: (a) G={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30}, (b) G={26,16,25,18,5,14,10,4,6,7,21,12,23,8,1,15,9,29,28,11,2,20,27,30,3,13,17,22,24,19}, and (c) G={19,22,18,13,10,28,7,15,17,8,30,12,26,11,20,9,27,21,25,6,29,1,23,5,3,24,16,14,4,2}. N=30. In all three insets, the values of ωj are plotted for given ω0=0 and δω=N. ... Coupled nonidentical oscillators
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Detection and manipulation of the qubit. (a) Fluorescence image of nanodiamond prepared on the CPW transmission line. NV S1 is circled. The inset is a photo of CPW with 20μm gaps fabricated on a silica glass. (b) CW ODMR spectrum for NV S1. The inset is energy levels of NV center. A 532nm laser is used to excite and initialize the NV center. Fluorescence is collected by a confocal microscope. (c) Rabi oscillation of NV S1. Rabi oscillation period is about 62ns. (d) Hahn echo and CPMG control pulse sequences. πx (πy) implies the direction of microwave magnetic fields parallel to x (y). ... Spectral density of the spin bath. (a) NV S1, (b) NV S2. All values of spectral density S(ω) of the spin bath are extracted from the CPMG data (blue points). Each blue data point represents a specific probed frequency ω=πn/t, in which n is the number of control pulses and t is the specific duration. The red points are the average values at a certain frequency. The mean spectral density is fit to the Lorentzian function (Eq. (3)) (green line). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.) ... Characterization of lifetime of NV center spins. (a) Ramsey interference of NV S1 (circle) and NV S2 (diamond). The oscillation in Ramsey signal originates from the beating among different transitions corresponding to the host three 14N nuclear spin states. The oscillation frequency of Ramsey signal is equal to microwave detuning from spin resonance. Solid lines ~exp[−(t/T2⁎)m] fit the experimental data points, where m is a free parameter. (b) Comparison of Hahn echo coherence time T2 of NV S1 (circle) and NV S2 (diamond). The solid lines are fits to ~exp[−(t/T2)p], in which p is a fit parameter.
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Microwave spectroscopy of a one-electron double dot. (a) Charge occupancy of the left dot, M, as a function of ε for several microwave frequencies. (b) One-half of the resonance peak splitting as a function of f for several values of VT. Solid lines are best fits to the experimental data using the theory outlined in the text. Inset: Two-level system energy level diagram. (c) Amplitude of the resonance, expressed as Mmax(τ)/Mmax(τ=5ns), as a function of chopped cw period, τ, with f=19GHz. Theory gives a best fit T1=16ns (solid line, see text). Inset: Single photon peak shown in a plot of M as a function of ε for τ=5ns and 1μs. (d) Power dependence of the resonance for f=24GHz. Widths are used to extract the ensemble-averaged charge dephasing time T2*. At higher microwave powers multiple photon processes occur. Curves are offset by 0.3 for clarity. ... Rabi oscillation... Spin qubit... Charge qubit
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Examples of a spike without HFOs (left) and a spike with HFOs (right), as defined with the Analytic Morse wavelet in the time–frequency domain. ... High Frequency Oscillations... Parameter selection for the Analytic Morse Wavelet; top: time–frequency presentation for different values of n (m=40), bottom: raw signal and filtered signal (80–250Hz). Blue lines represent HFO interval marked visually. ... Examples of detection errors. Left: HFO without isolated blob but having oscillation in the raw signal. Right: HFO without visible oscillation in the raw signal but representing an isolated peak. Blue lines show the HFO interval marked by reviewers. ... Time–frequency
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Qubit... (Color online.) Contour plots of the normalized decay rate γ(τ)/γ0 of the qubit only in the cavity bath, versus the time interval τ between successive measurements, and the central frequency ωcav of the cavity mode. (a) The width of the cavity frequency is λ=10−4Δ, and accordingly the cavity quality factor Q=104. (b) The width of the cavity frequency λ=5×10−3Δ, corresponding to the cavity quality factor Q=2×103. The region 1⩽γ(τ)/γ0⩽1.05 is shown as light magenta. The QZE region corresponds to γ(τ)/γ01. Evidently, a transition from the QZE to the AZE is observed by varying the central frequency of the cavity mode at finite τ (τ>0.6Δ−1 when Q=104, and τ>2.6Δ−1 when Q=2×103). ... (Color online.) Time dependence of the probability for the qubit at its excited state. In the resonant case, the parameters are ωcav=Δ=100g and τ=0.1g−1. In the detuning case, the cavity mode frequency is varied to ωcav=80g. Note that the successive measurements slow down the decay rate of excited state in the resonant case, which is the QZE. While in the detuning case, the measurements speed up the qubit decay rate, which is the AZE. ... The normalized effective decay rate γ(τ)/γ0 of the qubit for two quality factors Q when τ=5Δ−1, in the presence of both the cavity bath and the low-frequency qubitʼs intrinsic bath. ... (Color online.) (a) Sketch of a qubit with the spontaneous dissipation rate γ coupled to a cavity with the loss rate κ via a coupling strength g. (b) and (c) schematically show the bath density spectrum of the qubit environment: (b) the Ohmic qubitʼs intrinsic bath (green dashed) and the Lorentzian cavity bath (red solid), (c) the low-frequency qubitʼs intrinsic bath (green dashed) and the Lorentzian cavity bath (red solid). ... (Color online.) (a) Superconducting circuit model of a frequency-tunable transmission line resonator, which is archived by changing the boundary condition, coupled with a qubit. (b) Superconducting circuit model (1) of the effective tunable inductors, which are consisted of a series array of SQUIDs (2).
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Qubit... The oscillation period T0 changes with the temperature T and Coulomb bound potential β. ... The oscillation period T0 changes with the temperature T and electron phonon coupling strength α .
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Frequency spectrograms distribution along the axial direction (R/D=2). ... Frequency spectrograms of condensation oscillation [21]. ... Frequency spectrograms under radial position of R/D=3.0 and R/D=4.0. ... Half affected width of pressure oscillation. ... Pressure oscillation... Oscillation power axial distribution for low frequency region.
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